|
%I #4 Nov 29 2017 06:56:43
%S 1,2,2,4,11,4,7,29,29,7,12,80,104,80,12,21,261,467,467,261,21,37,789,
%T 2197,3472,2197,789,37,65,2354,9645,26544,26544,9645,2354,65,114,7199,
%U 43335,190943,333366,190943,43335,7199,114,200,21889,195508,1406191
%N T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 1 or 2 king-move neighboring 1s.
%C Table starts
%C ...1.....2......4........7.........12...........21.............37
%C ...2....11.....29.......80........261..........789...........2354
%C ...4....29....104......467.......2197.........9645..........43335
%C ...7....80....467.....3472......26544.......190943........1406191
%C ..12...261...2197....26544.....333366......3804661.......45214991
%C ..21...789...9645...190943....3804661.....68406015.....1296880337
%C ..37..2354..43335..1406191...45214991...1296880337....39611268638
%C ..65..7199.195508.10368395..538013975..24467737897..1200659717965
%C .114.21889.876170.76065766.6343699611.457692634063.36061398110075
%H R. H. Hardin, <a href="/A295847/b295847.txt">Table of n, a(n) for n = 1..311</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
%F k=2: a(n) = 3*a(n-1) -a(n-2) +6*a(n-3) -8*a(n-4)
%F k=3: [order 9]
%F k=4: [order 16]
%F k=5: [order 35]
%F k=6: [order 73]
%e Some solutions for n=4 k=4
%e ..1..0..0..0. .1..1..1..0. .0..1..0..0. .0..0..1..1. .0..1..1..0
%e ..1..0..1..1. .0..0..0..0. .1..0..0..1. .1..0..0..0. .1..0..0..1
%e ..1..0..1..0. .1..1..0..1. .0..1..0..1. .1..0..0..1. .0..1..0..0
%e ..1..0..0..0. .0..0..0..1. .0..0..1..0. .1..0..1..1. .0..1..0..0
%Y Column 1 is A005251(n+2).
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Nov 29 2017
| 